On a bitter, snowy Sunday last month, Douglas Elliman broker Suzanne Schein held an open house for a one-bedroom co-op on West Ninth Street. She expected maybe 10 people – but about 100 people showed up. The apartment got three offers, and it sold above the $590,000 asking price.

With just three hours’ notice for a Chelsea open house last week, 15 people braved the arctic temperatures – and five made offers. The one-bedroom was sold by Manhattan Residential’s Shai Shustik in just 45 minutes. The buyer paid the asking price, $350,000, in cash.

A rebounding economy and shrinking housing stock has led to increasingly vicious competition for the precious few properties available. Today, open houses – traditionally the leisurely, Sunday afternoon way to house-hunt – are becoming less like civilized people searching for a home than pigs fighting for a place at the trough.

“Open houses are wall-to-wall people,” says Patrick Lilly, managing director at Coldwell Banker Hunt Kennedy. “Everybody recognizes that the demand is so high – that’s what helps build the frenzy.”

According to a recent report from the Corcoran Group, there are now approximately 6,000 properties available in Manhattan – half the inventory available at this time last year.

“There’s just too many people walking through these properties,” says Michael Shapot, a manager at Coldwell Banker Hunt Kennedy. “I like the idea of bopping into open houses and seeing four, five things in one day. Now you can’t have that flexibility – it takes so much longer to see a property.

“It’s like going to Disney World and not going on every ride because the lines are too long.”

LAST weekend, just hours before the Super Bowl, NYP Home visited an open house for a two-bedroom, two-terrace condo in Chelsea, priced at $849,000.

Fifteen minutes ahead of schedule, a dozen anxious lookers were in the lobby. Within the first 20 minutes, 40 people walked through the 1,000-square-foot space.

“This is going to get sold today,” says Douglas Elliman’s Uri Hanoch, surveying the crowd, which, clad in a rainbow assortment of parkas, appeared more apres-ski cocktail party than open house.

“It’s a turnoff,” says Ajay Goyal, who has been home-shopping for more than a year. “I’m not that desperate.”

In all, approximately 100 people came by. There were eight offers – five above the asking price. There’s currently an accepted offer – for nearly $50,000 above the asking price – and four backups.

Like many properties sold after open houses, it was the first day it hit the market.

“It’s madness and hysteria out there,” says Darren Sukenik, senior vice president at Douglas Elliman, who handled the sale.

Of course, not every property causes a stampede. That same Sunday, NYP Home visited a few open houses; two did not have the clamor and crowds of the Chelsea apartment. At a $320,000 Sheridan Square studio, 35 people trickled in; none made offers. A Brooklyn Heights co-op – quite possibly the neighborhood’s only one-bedroom under $200,000 – brought out 12 people, but no offers.

In other words, don’t panic. “There’s no reason why you should step away from the market – you should just stay calm,” says Halstead Property president Diane Ramirez. “We’ve got a lot of buyers, and we may have limited product – but there is product.”

Nonetheless, for unique properties in prime locations – downtown and the West Side are especially hot – expect a stressed-out throng.

In an effort to control crowds, Coldwell Banker Hunt Kennedy assigns two agents to each open house. But sometimes that’s not enough. “Perhaps the solution is open house by appointment only,” says Shapot.

Yes, it’s an oxymoron – and an increasing reality.

“In some cases, buildings have been overwhelmed by the amount of people that are going through,” says Linda Stillwell, senior vice president at the Corcoran Group, who will host an appointment-only open house Monday for a two-bedroom Upper East Side co-op.

It’s also a way to separate serious buyers from weekend voyeurs. “It requires more of a commitment on the buyers’ part,” says Stillwell. “They have to make the effort to speak to the broker, rather than just be anonymous.”

Still, for even the most committed searchers, finding a home is akin to getting a table at Per Se – something nearly impossible to achieve.

Moira Ariev Butner and her husband, David, have spent months looking for a small two-bedroom in Manhattan.

Last week, Butner went to an open house for an affordable two-bedroom on West 79th Street. “We stopped by toward the end and there had already been over 100 people,” she says. “It was sheer insanity.”

The Butners made their best offer, but it wasn’t enough.

“There was an upside,” says Butner, trying to remain hopeful. “Despite all the mess, there were only eight serious offers.”

Additional reporting by Adam Bonislawski, Dori Fern and Dan Levine

FROM (OPEN) HOUSE TO HOME

IT’S a jungle out there – but don’t lose hope. Halstead Property’s Diane Ramirez offers sage advice on how to land a new home in the current ultracompetitve market:

1. Stay calm.

2. Go early.

3. Make like a Boy Scout and be prepared. If you need financing, bring a letter from your bank showing you’ve been preapproved for a mortage.

4. Find a quality real estate attorney, “somebody who understands the importance of turning around a contract in a day.”

5. Look the part. Wear classy, professional clothes and sellers will view you as a serious buyer.